Question

How to show the trace inequality of two P.S.D matrices $\text{Tr(X)}\leq\text{Tr(Y)}$ when $X \preceq Y$?

score 269 · Answer 1 · 2019-01-15 17:02:48

269

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How to show the trace inequality of two P.S.D matrices $\text{Tr(X)}\leq\text{Tr(Y)}$ when $X \preceq Y$?

Published on 15 Jan 2019 - 17:02

score 104 · Answer 2 · 2019-01-18 00:38:00

104

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Representation of negative Quantum entropy in terms of eigenvalues, i.e., $\text{Tr}(M\log M -M)=\sum_{i=1}^{n}(\lambda_i\log(\lambda_i)-\lambda_i)$?

Published on 18 Jan 2019 - 0:38

score 104 · Answer 3 · 2019-01-18 20:17:48

104

Views

How to show $\text{Tr}(M\log N)=\sum_{i,j}^n\lambda_i\log(\tilde{\lambda_j})(u_i^{\top}\tilde{u}_j)^2$?

Published on 18 Jan 2019 - 20:17

score 888 · Answer 4 · 2019-01-19 01:40:43

888

Views

Fourier Transform of $e^{-<x,Ax>}$, $A$ is a symmetric, positive definite matrix

Published on 19 Jan 2019 - 1:40

score 120 · Answer 5 · 2019-01-20 22:47:27

120

Views

Show a polynomial of degree 4 in 7 variables is positive

Published on 20 Jan 2019 - 22:47

score 827 · Answer 6 · 2026-03-25 10:52:47

827

Views

Largest eigenvalue of matrix product $A^T B A$

Published on 25 Mar 2026 - 10:52

score 142 · Answer 7 · 2019-01-27 21:51:49

142

Views

Positive Definiteness of Arcsin of a Positve Definite Matrix

Published on 27 Jan 2019 - 21:51

score 86 · Answer 8 · 2019-01-31 03:20:47

86

Views

Defining Hermitian Adjoints Non-degenerate Hermitian Forms that are NOT positive definite.

Published on 31 Jan 2019 - 3:20

score 2.8k · Answer 9 · 2026-02-27 21:32:11

2.8k

Views

Checking if matrix $A$ is positive definite via Cholesky decomposition

Published on 27 Feb 2026 - 21:32

score 390 · Answer 10 · 2019-01-31 19:59:06

390

Views

Compare ratio of two determinants before and after adding sum of rank 1 matrices in both determinants

Published on 31 Jan 2019 - 19:59

score 112 · Answer 11 · 2026-03-25 01:23:50

112

Views

how to prove the following linear matrix inequality

Published on 25 Mar 2026 - 1:23

score 63 · Answer 12 · 2019-02-03 17:08:49

63

Views

Principal Minor Theorem for dimension 2

Published on 03 Feb 2019 - 17:08

score 68 · Answer 13 · 2019-02-06 08:07:07

68

Views

How to prove that $\langle P,A^2 \rangle \le 0 $ for every positive $P$ and skew-symmetric $A$?

Published on 06 Feb 2019 - 8:07

score 3k · Answer 14 · 2019-02-07 15:54:55

3k

Views

Inequality for trace of product of matrices

Published on 07 Feb 2019 - 15:54

score 14.9k · Answer 15 · 2026-03-25 10:53:04

14.9k

Views

How to show that this matrix is positive semidefinite?

Published on 25 Mar 2026 - 10:53

List Question

How to show the trace inequality of two P.S.D matrices $\text{Tr(X)}\leq\text{Tr(Y)}$ when $X \preceq Y$?

Representation of negative Quantum entropy in terms of eigenvalues, i.e., $\text{Tr}(M\log M -M)=\sum_{i=1}^{n}(\lambda_i\log(\lambda_i)-\lambda_i)$?

How to show $\text{Tr}(M\log N)=\sum_{i,j}^n\lambda_i\log(\tilde{\lambda_j})(u_i^{\top}\tilde{u}_j)^2$?

Fourier Transform of $e^{-<x,Ax>}$, $A$ is a symmetric, positive definite matrix

Show a polynomial of degree 4 in 7 variables is positive

Largest eigenvalue of matrix product $A^T B A$

Positive Definiteness of Arcsin of a Positve Definite Matrix

Defining Hermitian Adjoints Non-degenerate Hermitian Forms that are NOT positive definite.

Checking if matrix $A$ is positive definite via Cholesky decomposition

Compare ratio of two determinants before and after adding sum of rank 1 matrices in both determinants

how to prove the following linear matrix inequality

Principal Minor Theorem for dimension 2

How to prove that $\langle P,A^2 \rangle \le 0 $ for every positive $P$ and skew-symmetric $A$?

Inequality for trace of product of matrices

How to show that this matrix is positive semidefinite?

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